Pertanyaan

Selesaikan ∫ ( 3 x − 5 ) 12 d x

Selesaikan $\int (3 x - 5)^{12} d x$

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

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integral open parentheses 3 x minus 5 close parentheses to the power of 12 d x equals 1 over 39 open parentheses 3 x minus 5 close parentheses to the power of 13 plus C

Pembahasan

Integral tersebut dapat diselesaikan dengan metode substitusi seperti di bawah ini Misalnya Maka Jadi .

Integral tersebut dapat diselesaikan dengan metode substitusi seperti di bawah ini

Misalnya

$u equals 3 x minus 5 space rightwards double arrow straight d u equals 3 straight d x space space space space space space space space space space space space space space space space space rightwards double arrow straight d x equals fraction numerator straight d u over denominator 3 end fraction$

Maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 3 x minus 5 close parentheses to the power of 12 d x end cell equals cell integral u to the power of 12 fraction numerator straight d u over denominator 3 end fraction end cell row blank equals cell 1 third integral u to the power of 12 straight d u end cell row blank equals cell 1 third times fraction numerator 1 over denominator 12 plus 1 end fraction u to the power of 12 plus 1 end exponent plus C end cell row blank equals cell 1 third times 1 over 13 times u to the power of 13 plus C end cell row blank equals cell 1 over 39 u to the power of 13 plus C end cell row blank equals cell 1 over 39 open parentheses 3 x minus 5 close parentheses to the power of 13 plus C end cell end table$

Jadi integral open parentheses 3 x minus 5 close parentheses to the power of 12 d x equals 1 over 39 open parentheses 3 x minus 5 close parentheses to the power of 13 plus C .